Topicm6d79b9270767a3fd_1528449000663_0Topic

Increasing linear function, decreasing linear function

Levelm6d79b9270767a3fd_1528449084556_0Level

Third

Core curriculumm6d79b9270767a3fd_1528449076687_0Core curriculum

V. Functions. The student:

4) reads from the graph of the function: the domain, the range, roots, monotonic intervals, intervals in which the function takes values not greater (not smaller) or smaller (not greater) than a given number, greatest and smallest values of the function (if they exist) in the closed interval and arguments for which the function takes greatest and smallest values.

Timingm6d79b9270767a3fd_1528449068082_0Timing

45 minutes

General objectivem6d79b9270767a3fd_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm6d79b9270767a3fd_1528449552113_0Specific objectives

1. Identifying relations between slopeslopeslope of the function and monotonicity of the function.

2. Determining the monotonicity of the function.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm6d79b9270767a3fd_1528450430307_0Learning outcomes

The student:

- identifies relations between slope of the function and monotonicity of the function,

- determines the monotonicity of the function.

Methodsm6d79b9270767a3fd_1528449534267_0Methods

1. Discussion.

2. Mental map.

Forms of workm6d79b9270767a3fd_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm6d79b9270767a3fd_1528450127855_0Introduction

The teacher asks chosen students to revise information about linear function.

Students also revise vocabulary related to the monotonicity of functions.

The teacher introduces the subject of the lesson – relation between the monotonicity of the function and its slopeslopeslope.

Procedurem6d79b9270767a3fd_1528446435040_0Procedure

Group work – students write a few formulas of linear functions and draw plots. Based on plots they determine whether the function is increasing, decreasing or constant.

They try to identify the relation between the monotonicity of the function and the sign of its slope. They verify their theories by analysing the slideshow.

Task
Students create mental maps on which they illustrate obtained information about the monotonicity of linear function. Representatives of groups present maps and discuss most important elements.

[Slideshow]

They point out that a linear function described with the formula f(x) = ax + b is:

- increasing when slopeslopeslope a is a positive number,

- decreasing when slope a is a negative number,

- constant when slope a is equal to 0.

Students use obtained information in the exercises.

Task
Find the equation of the line that goes through points $A(5,\sqrt{3})$ and $B(-2,\sqrt{3})$. Determine monotonicity of the function whose plot is this line.m6d79b9270767a3fd_1527752263647_0Find the equation of the line that goes through points $A(5,\sqrt{3})$ and $B(-2,\sqrt{3})$. Determine monotonicity of the function whose plot is this line.

Task
What condition must the number m meet so that the function f described by the formula f(x) = (4 - m)x + 2m is increasing?

Task
Give formula for the decreasing function that crosses axis Y in the point (0, 7), and its root is 2m6d79b9270767a3fd_1527752256679_0Give formula for the decreasing function that crosses axis Y in the point (0, 7), and its root is 2.

The teacher evaluates students’ work and clarifies doubts.

An extra task:
Give an example of a linear function whose range is a set of one element. Determine the monotonicity
of the function.

Lesson summarym6d79b9270767a3fd_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

A linear function described with the formula f(x) = ax + b is:

- increasing when slopeslopeslope a is a positive number,

- decreasing when slope a is a negative number,

- constant when slope a is equal to 0.

Selected words and expressions used in the lesson plan

constant functionconstant functionconstant function

decreasing functiondecreasing functiondecreasing function

increasing functionincreasing functionincreasing function

monotonicity of the linear functionmonotonicity of the linear functionmonotonicity of the linear function

slopeslopeslope